You can't normally create alerts for SharePoint groups. Here's how:
- E-mail enable the SharePoint group so that a distribution list/group is created in Active Directory.
- Edit the properties of the group to change its Group Type to Security. Only security groups will show up in SharePoint's address book. They will show up as "domain groups" in SharePoint.
- Give the domain group at least visitor permissions on the list that are you are creating the alerts for. Alerts won't be sent if the domain group doesn't have appropriate permissions. This will mean that you'll likely have both the SharePoint group and the domain group in the permissions list. Simply giving the SharePoint group permissions is not enough.
- Then setup the alert and use the address book to locate the domain group. In the address book you'll see it with the form "DOMAIN\group name".
- Now test out your alerts. If you have require approval turned on for the list, make sure you approve the items so alerts will be sent.